Question

8) a. Suppose a 7.2% semi-annual coupon 20-year Treasury issue with a par value of $100 issue is priced in the market based on the on-the-run 20-year Treasury yield. Assume further that this yield is 5.60%, so that each cash flow is discounted at 5.60% divided by 2. What is the market price of the Treasury issue based on this assumption?

b. Suppose also that the price of the same Treasury issue would be $115.285 if it is calculated based on the prevailing Treasury spot rate curve. What action would a dealer take and what would the arbitrage profit be? Can this situation persist in the long run?

Answer 1

8a)

Using a financial calculator

FV = 100

PMT = 3.6 (7.2%/2 = 3.6% on face value 100)

N = 40 (20years*2 payments per year = 40 periods)

I/Y = 5.60/2

cpt PV, we get PV = 119.104

Hence, market price of the Treasury issue is $119.104

8b)

The price of the treasury issue is lesser than the calculated price of the issue (based on yield). Hence, the dealer would buy the treasury issue at $115.285 and would sell the issue at market price of $119.104.=

Arbitrage profit = $119.104 - $115.285 = $3.819

No, this situation cannot persist in the long run since market participants would quickly exploit the arbitrage situation and the issue price would trade at the market price quickly, thus destroying any further arbitrage possibility.